Medical syringes are used in both injection and aspiration modes. Conventionally, when a syringe is used to inject medicine via a needle into a vein or the like, the operator holds the syringe in one hand and squeezes the plunger into the syringe cylinder using the thumb and fingers of the same hand. However, when a syringe is used to aspirate or withdraw blood or other fluid from a needle inserted in a vein or the like, the operator must use two hands, typically holding the cylinder in one hand while pulling the plunger out of the cylinder with the other hand. The present invention overcomes these difficulties by providing a medical syringe which can be held and operated in one hand for both injection and aspiration.